Have an
Irrational Day
3.14
AuT(
g
0
Austin Storey
3-142013
Math 1060
The Importance of Pi
Since the construction of the Great pyramids (2589 BC), p1 has been used to represent
the formulated area of a circle. Throughout history, many mathematicians and architects have
used pi to conduct measurements as well as provide the world with a better understanding of
using exactness in everyday tasks. It wasn’t until 1706 when a mathematician named William
Jones proposed the pi symbol
(
rt),
which happens to be the internationally known symbol for
the value of pi.
For Centuries p1 has been an essential constant in being able to make exact
measurements of the area of a circle. This idea especially applies in mathematics, physics,
thermodynamics, mechanics, etc. During the
th
15
and lG centuries, mathematicians
th
attempted to calculate the value of pi to around the 50
decimal place. Now in the
th
20
and
st
21
centuries, computers are able to calculate pi up to the trillionth digit. An interesting fact about
pi that is not found in other numbers is that while pi has a never ending number of decimals, at
the same time it does not reach a point where it repeats or a place where it has a pattern of
repetition. All of the numbers contained in pi are completely different and do not have a
specific trend in value.
While pi has yet to be completely simplified or quantified, it has still shaped a majority
of the sciences in the world today. I decided to make a plate that lists the symbol, as well as
the first 17 digits of pi. It is a circular object, therefore it will follow the circumference to
diameter ratio that all circles follow. The plate is just another example of how a common
household object is more complex that meets the eye.
Kevin Larsen
U058361 1
Pi Day 2013
In honor of Pi Day, I learned how to make 2 different kinds of pies:
First, for dinner, I made a Pizza Pie. To help add to the festivities, I put the pepperonis on
the pizza in the shape of the Pi symbol. For dessert, I made chocolate pudding “pi.”
While the pizza was cooking and the pie was setting in the fridge, I made a border for the
table consisting of the first few numbers of Pi. After the timer on the oven went off, we
enjoyed our pizza pie.
For dessert, we decided to go to a neighbor’s and share this event with friends. While our
friend, SanShi, ate her piece of pie, I taught her about the importance of Pi and how it
became famous as a day of celebration.
Overall, Pi Day was a great success and fun event for the Larsen Family.
Project of Pi
Qixin Han
U0824570
‘—.
S
-Th
‘
5’
-•---
S
SS’1-I..1
In the Spring Break, we have Pi day. 11=3.1415926
LONG..
In this project, I will talk about the Pi with life.
Truth is often defined as consistent with fact or reality.
This sentence I understand to become consistent with subjective feeling and objective
should be better. According to the subjective and objective two concept can describe
the truth existing in the process. Mainly use the concept of PT, an absolute circular is a
subjective creation, the reality there is no absolute circle, but according to the need of
the fact that it is necessary from different sizes of round absolutely find out a rule to
undo the absolute size of different circles. According to the formula to calculate PT is
an unlimited circulating decimal, the results will be a very interesting phenomenon. If
someone asks you a PT is what you really can’t put the PT complete tell what a person
is, but only with the aid of other abstract concepts or formula to tell another PT is how
to. This and a lot of people say truth only needs cannot talk how consistent.
Mathematical concept is perfect. Abstraction is the concept of the absolute
circular exist, even this and other aspects of the mathematics, any concept actually is
trying to draw an absolute circular. Emotions such as absolute circular, absolute round
work and so on, its just different in different parts of the picture or big or small, big or
small is expressed as covering areas and connotation. In these areas a PT so that things
will only get more complicated.
Why do PT no end? This is because people want from a perfect things inside a
general rule, you will never ending like PT, which I understand to abstract away from
-
reality as according to the concept of must pay the price. The reality actually doesn’t
have that thing inside. So, this like everything about a person is cycle. It is a circle, a
Pi.
Love into the P1! Two circular meet how complex, who let you to imagine
something that is perfect? How much your relationship to the decimal places?
Life into the PT! Abstracts a circle, many people even life or get a happy life is
very difficult, so you do not worry it.
So, I think everybody should face to themselves. Know both ourselves and our
adversaries. When you are old, even you can’t move. That is the aim in your life.
Because of the P1 is a circle. The circle can be rolling.
This is my P1, also my life and everybody who are familiar with me.
4
A Short History of pi
3. 1415926535897932384626433832795028841971693993751058209749445
923078164062862089986280348253421170679821480865132823066470938
44609550582231725359408128481117450284102701938521105559644
6229489549303819644288109756659334461284756482337867831652
7120190914564856692346034861045432664821339360726024914127
3724587006606315588174881520920962829254091715364367892590
3600113305305488204665213841469519415116094330572703657595
9195309218611738193261179310511854807446237996274956735188575
2724891227938183011949129833673362440656643086021394946395224
73719070217986094370277053921717629317675238467481846766940513
20005681271452635608277857713427577896091736371787214684409012
24953430146549585371050792279689258923542019956112129021960864
03441815981362977477130996051870721134999999837297804995105973
17328160963185950244594553469083026425223082533446850352619311
88171010003137838752886587533208381420617177669147303598253490
42875546873115956286388235378759375195778185778053217122680661
30019278766111959092164201989380952572010654858632788659361533
81827968230301952035301852968995773622599413891249721775253479
13151557485724245415069595082953311686172785588907509838175463
74649393192550604009277016711390098488240128583616035637076601
04710181942955596198946767837449448255379774726847104047534646
2080466842590694912933136770289891521047521620569660240580381
5019351125338243003558764024749647326391419927260426992279678
2354781636009341721641219924586315030286182974555706749838505
4945885869269956909272107975093029553211653449872027559602364
806654991198818347977535663698074265425278625518184175746728
909777727938000816470600161452491921732172147723501414419735
685481613611573525521334757418494684385233239073941433345477
6241686251898356948556209921922218427255025425688767179049460
16534668049886272327917860857843838279679766814541009538837863
609506800642251252051 173929848960841284886269456042419652850222
106611863067442786220391949450471237137869609563643719172874677
Anthony Nowling
U0723940
Anthony Nowling
U0723940
The history of P1
Throughout time there have been many different theories of how pi came to be what it
is today. It is hard to tell for sure but the current theory suggests that it came into play when
there was a need for people to stay in one place for extended periods of time due to farming.
Today there is no evidence of when this was first started but it is believed that the value of p1
that they were using depended on the civilization. In Babylon they used 3 1/8, Egypt used
(16/2)’2, China used 3, and the Hebrews used 3. Since each place had their own value of Pi it
suggests that the people came up with this number on their own for the purpose of engineering
town buildings.
The first person on record that figured this number out was from Greece. He used it in
an equation that was called squaring the circle which involved a way to relate the area of a
circle to a square. The man that was trying to do this was named Anaxagoras around 400 BC.
Since Greece was the first to figure this out for sure due to our records, it explains why they
have come up with a lot of different types of math that we still use today.
After pi was created it spread across the world by scholars who studied in the University
at Alexandria which was considered to be the knowledge capital of the world at this time. One
important person studied in this University by the name of Archimedes. Archimedes was the
one who came up with the value that was use today which was 22/7. After Archimedes made
this number the Romans soon conquered Syracuse and the number was lost for many years in
Europe and it was not used for many years.
Meanwhile in other parts of the world pi was much more important than Europe while
they were in the dark ages. In the Mayan civilization they used pi for astronomy. Most
historians believe that the Mayan value was more accurate than the value that the Europeans
came up with. The Mayans were known for their architecture and building skills which explains
why they needed to create a value of pi that was precise.
Another civilization that came up with a version of pi was the Chinese. They discovered
the number about the same time as Europe but it was not as accurate. This statistic is one that
doesn’t make sense because they were known for their detailed architecture in their buildings.
This is not the end of pi.
At the start of the Renaissance there was much more activity with the calculation of pi.
This was sparked by navigation of the world and by the introduction of Arabic numerals. During
this period Leonardo Da Vinci surprisingly was not very influential to the cause. The
mathematicians involved in the progress of pi were Snellius, Gregory, and John Machin who
created formulas so it was possible to calculate faster than ever before. After this time the only
improvement that needed to be done to this effort was the speed in which it could be
calculated.
In the 1700’s calculus was invented by Isaac Newton which made the calculation of this
number the fastest to date and it was also proved to be irrational in France and Switzerland.
Since then we have been making pi more and more accurate. In 1949 there was a computer
that was called ENIAC which could calculate this number to 2,037 digits. Now there is a
computer that is located in Tokyo that can compute this number to 206,158,430,000 digits
which is currently the record. Currently, there is no end in sight for the exploration of pie.
Included in this paper is a graph that shows that extent of the progress that we have made in
the digits of pi due to better and better computers and better algorithms to calculate it out.
Record approximations of pi
1014
1012
In
4.’
1010
1o
106
io
100
2000
BCE
250
BCE
480
1400
1450
1500
1550
1600
1650
Year
1700
1750
1800
1850
1900
1950
2000
4
References
Thinkquest (2001) You Piece of the P1. [online] Available at: http:/Ilibrary.thinkquest.org/C01 lOl95lhistory/history.html
[Accessed: 15 Mar 2013].
Eymard, Pierre; Lafon, Jean Pierre (1999). The Number P1. American Mathematical Society. English translation by
Stephen Wilson.
Pi is Everywhere
When March l41 comes around,
Where can P1 be found?
Well there is no need to ask,
It is quite an easy task.
For 3.14 can be easily seen,
Much easier than a magic bean,
All you need to do,
Is make sure you tie your shoe,
And take a look,
Maybe at your desk or a book,
Because Pi is everywhere!
And this is my dare,
4 comes around,
That when March l
You make sure P1 is found.
By Scott Khuu
*The following pictures were all taken in my dorm room. This is to illustrate the
importance of p1 goes unseen in our daily Lives. I enjoyed doing this project. Thank
you Ms. Babenko©
V
c-I&V
P1 History
Ptolemy
(c. 150 AD)
3.1416
Zu Chongzhi
(430-50 1 AD)
355/1 13
al-Khwarizmi
(c. 800)
3.1416
al-Kashi
(c. 1430)
14 places
(1540-1603)
Viète
9 places
(1561-1615)
Roomen
17 places
35 placesExcept for Zu Chongzhi, about whom next to nothing is
Van Ceulen (c. 1600)
known and who is very unlikely to have known about Archimedes’ work, there was no
theoretical progress involved in these improvements, only greater stamina in calculation. Notice
how the lead, in this as in all scientific matters, passed from Europe to the East for the
millennium 400 to 1400 AD.
A1-Khwarizmi lived in Baghdad, and incidentally gave his name to ‘algorithm’, while the words
aljabr in the title of one of his books gave us the word ‘algebra’. Al-Kashi lived still further east,
in Samarkand, while Zu Chongzhi, one need hardly add, lived in China.
The European Renaissance brought about in due course a whole new mathematical world.
Among the first effects of this reawakening was the emergence of mathematical formulae for it.
One of the earliest was that of Wallis (16 16-1703)
2/it = (1.3.3.5.5.7. ...)/(2.2.4.4.6.6.
...)
and one of the best-known is
=
1
-
1/
+
1/5
-
1
+
This formula is sometimes attributed to Leibniz (1646-1716) but is seems to have been first
discovered by James Gregory (1638- 1675).
These are both dramatic and astonishing formulae, for the expressions on the right are
completely arithmetical in character, while it arises in the first instance from geometry. They
show the surprising results that infinite processes can achieve and point the way to the wonderful
richness of modem mathematics.
From the point of view of the calculation of it, however, neither is of any use at all. In Gregory’s
series, for example, to get 4 decimal places correct we require the error to be less than 0.00005 =
1/20000, and so we need about 10000 terms of the series. However, Gregory also showed the more
general result
tang x = x x
/3
3
-
+
/5
5
x
-
...
(-1 <x
1)
.
.
.
(3)
from which the first series results if we put x = 1. So using the fact that
)
3
tan’(’/
6
it!
=
=
6
it/
(‘/)(l
-
we get
1/(3.3)
+
11(5.3.3)
-
1/(7.3.3.3)
+
th
which converges much more quickly. The 10
term is 11(19 x
and so we have at least 4 places correct after just 9 terms.
), which is less than 0.00005,
J
9
3
An even better idea is to take the formula
=
)
2
tan’(’/
+
)
3
tan’(’/
(4)
and then calculate the two series obtained by putting first
1/2
and the
/3
into (3).
Clearly we shall get very rapid convergence indeed if we can find a formula something like
‘Jt14
=
tan’(’/a) +
tan’(’/b)
with a and b large. In 1706 Machin found such a formula:
=
(’/
1
tan
)
4 tan’(’/) 239
—
.
.
.
(5)
The more detail information:
Except for Zu Chongzhi, about whom next to nothing is known and who is very unlikely to have known
about Archimedes’ work, there was no theoretical progress involved in these improvements, only
greater stamina in calculation. Notice how the lead, in this as in all scientific matters, passed from
Europe to the East for the millennium 400 to 1400 AD.
Al-Khwarizmi lived in Baghdad, and incidentally gave his name to ‘algorithm’, while the words aT jabr in
the title of one of his books gave us the word ‘algebra’. Al-Kashi lived still further east, in Samarkand,
while Zu Chongzhi, one need hardly add, lived in China.
The European Renaissance brought about in due course a whole new mathematical world. Among the
first effects of this reawakening was the emergence of mathematical formulae for it. One of the earliest
was that of Wallis (1616-1703)
2/n
=
(1.3.3.5.5.7. ...)/(2.2.4.4.6.6.
...)
and one of the best-known is
n/4=1-1/3+1/5-1/7+....
This formula is sometimes attributed to Leibniz (1646-1716) but is seems to have been first discovered
by James Gregory (1638- 1675).
These are both dramatic and astonishing formulae, for the expressions on the right are completely
arithmetical in character, while it arises in the first instance from geometry. They show the surprising
results that infinite processes can achieve and point the way to the wonderful richness of modern
mathematics.
From the point of view of the calculation of it, however, neither is of any use at all. In Gregory’s series,
for example, to get 4 decimal places correct we require the error to be less than 0.00005 = 1/20000, and
so we need about 10000 terms of the series. However, Gregory also showed the more general result
tan-lx=x-x3/3+x5/5-...(-1x1)
..
.(3)
from which the first series results if we put x
tan-1(1/x!3)
rt/6
=
=
=
1. So using the fact that
n/6 we get
(1/V3)(1 1/(3.3)
-
+
1/(5.3.3) 1/(7.3.3.3)
-
+
which converges much more quickly. The 10th term is 1/(19 x 39\13), which is less than 0.00005, and so
we have at least 4 places correct after just 9 terms.
An even better idea is to take the formula
rt/4=tan-1(1/2)+tan-1(1/3)
.
.
.(4)
and then calculate the two series obtained by putting first 1/2 and the 1/3 into (3).
Clearly we shall get very rapid convergence indeed if we can find a formula something like
rt/4
=
tan-1(1/a)
+
tan-1(1/b)
with a and b large. In 1706 Machin found such a formula:
t/4
=
4 tan-1(1/5) tan-1(1/239)
-
.
.
.
(5)
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Adam Kiawe
U0709115
Easy as Pi
The man Einstein was great,
I really must state
He found such a number
It makes me wonder.
Oh what a number,
It makes me just plunder
In thought about that
And thought about this.
Three point one four one five nine
Makes the lazy student whine,
It works for me like a dime
And I can turn my work in on time.
Lots and lots cry
But learn the right way,
And give it a try.
You’ll se it’s easy as pi!
It helps me find area
Of circles and more.
It’s really that easy
That is for sure.
Peter Meirose
u0848294
A Quick History of P1
The earliest known calculations of Pi were found to be around 1600 BCE by the Babylonians
calculations of 3.125, where as the bible holds a ratio of 1:3 and the ancient Egyptians had
[(8d)/9]squared.
Archimedes, was able to figure out the area of a circle by using polygons with as many as 96 sides
Archimedes figured out that the more sides a shape had the closer he could come to the area of the
circle.
Some of the Early European Mathematicians such as James Gregory were able to come up with
Pill 1/3+1/5-1/7
-
In 1706 John Machim refined Gregory’s Pi formula, which is still used by computer programmers to
compute pi
=
4 arctan
1
—
arctan
1
The symbol for Pi was introduced William Jones, a British mathematician, in 1706 and later adopted
as the universal symbol for 3.14....
j LI
The Importance of P1
Amy Thomson
Math 1060
Pi is an irrational number that denotes the ratio between the circumference of a circle
and its diameter. P1 literally goes on forever and is often approximated as 3.14159 in decimal
form. The Greek symbol for pi is ir, and has been used ever since the 18th century!
The earliest known origins of pi actually stem from areas such as Egypt and Babylon. The
Egyptians and Babylonians often used geometry to explore the strange enigma of pi. The name
pi came originally from Greeks, who established the symbol rt. This lead to the Latin
pronounciation “p1.”
Pi is an irrational number that never ends. There doesn’t seem to be any obvious
pattern among the numerical digits of pi. These strange properties drove some mathematicians
and philosophers to suicide because there was no way to find the end of pi. P1 cannot be
written as a simple fraction, only a continued fraction. Pi is what ties all circles together, no
matter their size, the ratio of the circumference to the diameter will always equal 3.14159.
Pi is extremely important in mathematics because it is used in so many different ways,
mostly regarding circles. For example, pi is used to calculate the area of a circle, which
is essential to mathematics and deserves to be celebrated.
is
. P1
2
rtr
Allison Wiechmann u0742237
Pi Extra Credit!
So this picture may not look like much, but it occurs everywhere in nature and is calculated with
PH This pi symbol is made from decaying Redwood and Redwood pine cones because I went to the
Redwood Forest for spring break. Pine cones and tree rings can are two natural objects that have the
Golden Section! The Oberg Formula is the formula which connects Archimedes’ constant (pi) to the
Golden Section! This is so cool because Archimedes nailed down p1 unlike in the past where other
regions of the world were slightly off. From that, Oberg and Johnson developed the set of Fibonacci
numbers:
tPhi
=
22
1
+
—
+
[(2/3) / (Fl +F2Phj)
+
(1/5) / (F3+F4Phi) (1/7) / (F5+F6Phi)]
-
[(2/9)/(F7+F8Phi)+(1/11)/(F9+FlOPhi)-(1/13)/(F11+Fl2Phi)]
[(2/15)/(F13+Fl4Phi)+(1/17)/(F15+Fl6Phi)-(1/19)/(F17+Fl8Phi)]
—...J
=
5.083203692....
Pi is related to the Golden Section(phi) using trigometric functions in which the Oberg Formula which is
styled from:
—
=
arctgtj;’::)
)
3
arctg(phi
when x=1
0
cr
rJ)
C
C
cr
?ZZA
p
1
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u0718364
Ahmed Dahir
03/17/13
Math 1060
P1 Project
What is the significant of pi?
Is it a great thing or something found in sci fi?
Pus a Greek letter used in math;
Not the thing you eat and cut up in 8th, 4th, or Half’s;
Pi is use to find the circumference or area of a circle;
You can also use it to find the area of the glasses lens that
belongs to Steve Urkel;
Treat a circle like a lock door,
And the key to the lock is 3.14
g,qsa4q(.11s4s ØiSi33
4,
.
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.,‘
OVflOcq
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•
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-
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a-.
.
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Ted Wallace
u0493402
P1
In order to gather a better understanding of Pi, I went out and rented the book Here’s Looking
at Euclid from the local library and I read its section on the subject. My ignorance on the subject as a
college student truly showed its self when I began reading what exactly pi is on a circle and how/why the
digits continue on infinitely. I was greatly taken aback by the amount of effort and methodology over
the centuries that people have spent and utilized in order to figure out Pi. I decided since they were
extremely fascinating to me, I’d explain here how the initial digits were discovered and also throw in a
few humorous (to me, anyway) photos and comics at the end.
P1 is, simply put, the ratio of the diameter to circumference of a circle. The diameter always fits
exactly 3 times plus a little more around a circle. The first great thinker who was able to created a
“tool” defining pi was Archimedes and tool was rather simple but effective. He drew two hexagons
around a circle with a diameter of 1 unit, one on the inside and one on the outside. He took the
perimeter of these two hexagons and the outside to be 3.46 and the inside to be 3. This meant that pi
had to lie somewhere in between. By adding more and more sides to these polygons they were able to
define pi to about 35 decimal places accurately.
While studying up on pi, I found that these decimal places to which we have taken p1, really
don’t matter. According to the book,
-
-
“There is no practical reason to know pi to 72 digits, or to 35 digits for that matter. Four decimal
places are enough for the engineers of precision instruments. Ten decimal places are sufficient
to calculate the circumference of the Earth to within a fraction of a centimeter. With 39 decimal
places, it is possible to compute the circumference of a circle surrounding the known universe to
within an accuracy of a radius of a hydrogen atom.”
Here are a few photos I found that made me laugh on p1 day:
• • • ••.• •• • •. I I•
Mind
Blown
D
D
I
I
(j1)\
vri
t2/
•)(
JPELOT
IN 1!N 2 UxM2t iMzc3IN DMyY nwwLjt =
https://doc-Ut-3t-docsviewer.googIeusercontent.com/vi
Name: Abdulaziz Alowavved
Trig IObO-004
Instructor: Vera Babenko
Date: Mar I8’, 2013
P1=3. 14(t)
What Is
it?
Most of the definitions that have been advanced so far define
t
as the ratio of the
perimeter of a circle and its diameter. If one measures the perimeter of any circular object and
divides that value by its diameter, one is bound to obtain a constant figure, presently
approximated as 3.14 (flergen, Borwein & Borwein, 2004). This figure is often characterized
as irrational arid transcendental. However, this figure has always been 3. 14; changed slitly in
the hands of different mathematicians in histoty before assumingthis value. In order to
understand its origin, an evaluation of a short history oft would be inerative.
History of it
Accordingto Bergen et al. (2004),fl has been in existence for thousands of years. In
fact, it dates back to biblical times as evidenced in 1 King VII: 23. Hebrew builders required the
relationship between a square and a circle in order to build
pemanent
building. Consequently,
Hebrews and Chinese approximated the value of Pi to be three 1iile the Babylonians
approximated the value to 3. 125.
The first mathematical evaluation of t was initiated in 400B.C by a Greek
mathematician, Anaxagoras. He attempted to find the relationship between the area of square
and that of the circle, With Alexander the Great conquests, the Greek culture spread all the way
to Eg?pt, during which time Egypt was transformed into an intellectual center. It is then that a
flttps://doc-W3--cIocsv1ewer.googIeusercontent.comJv1
IN kIN 2 UxM2tiMzc.3iN DMyYnwwLJL =
gyeat mathematician,
Fuclid, published Elements, a vital resource for future evaluations ofx.
Archimedes was the first to advance the modern approximation of
t.
Througji various
experiments he concluded that the most reasonable approximation ofit was 223/ 71 which was
assumed to be 22/7
Future mathematicians would invent different ways of approximating t. For instan ce, James
Gregory advanced the arithmetic formulae for calculation of
it
4
=1-
t.
This was
111
+ —
357
The lenh conutation was later sinlified
by John Machin, who replaced the above formula
v ith:
It
=
4arctan(
I
5
4
)— arctan(
239
)
With the invention of the conuter, the precision of calculation oft has changed siiificantly.
The FAC’ con)uters developed in the mid twentieth century could conute the value ofPi to
2O37digits. Modem computers can calculate the value to a precision of 20b,158,430,000 digits.
Uses of it
For basic elementary mathematics,
t
is the value used in computing the area or circumference of
a circle, For instance, the formula for corrputing the region of a circle is given by:
Area= tr where r is the radius of the circle.
,
If the circle has a radius
=
3un its, then the Area is given by:
Area=
*
9 3 14
Area’
On the
=
2
28. 2bznzits
other hand, the perimeter of a circle is given by:
IN il’ 2J muUcwIvIz2 IN mu J1N iWWLJtI =
flLLPS ://aOC-Ug-dI-aOCSVieWer.gOOg1eUSerCOflEeflE.COrfl/Vi
Zac Marion
U0664739
As I sat there on P1 Day wondering how I was going to pass off eating a slice of apple pie as
actual “P1 Day extra credit”, I began to think about the connections that could be made to pie.
Sure, it’s obvious shape could be used, divided into the standard P1 measurements, and I could
then decidehowmanyof thesections Iwould eat. 1/2it?m??2jt?l?l? I mean, I’m afattyand I
love dutch apple pie so I’m capable of eating the whole thing.
But the more I thought about the connections, the more I realized that Hacked a great deal in
knowing the history of Pi and where, or even when, it came to be. I decided that the beneficial
project that I could do for myself would be to investigate the history and origins of Pi... while I
ate my pie. That’s a win/win situation.
The diameter of a circle isthe distance from edge to edge, measuring straightthrough the
center. The circunference of a arcie is the distance around. Pi (it) is the ratio of a circle’s
circumference to its diameter. P1 is a constant nuriter, meaning that for l circles, regardless ol
size, P1 will be the same.
By measuring circular objects, it has always turned out that a cirde is a little more than 3
times itswidth around. In the Old Testament ofthe Bible (1 Kings 7:23), a circular pool is
referred to as being 30 cubits around, and 10 ojbits aoss. The earliest written approximations
of it are found in Egypt and Babylon, both within 1 percent of the true value. In Babylon, a day
tablet dated 1900—1600 BC has a geometric statement that, by implication, treats it as 25/
8=3.1250. In Egypt,the Iiind Papyrus, dated around 1650 BC, but copied from a document
dated to 1850 BC has a formula for the area of a circle that treats it as (16/9)2 3.1605.
The mathematician Archimedes used polygons with many sides to approximate cirdes and
determined that P1 was approximately 22/7. The symbol (“it”, from the Greek alphabet) was
first used in 1706 by William Jones. A ‘p’ was chosen for ‘perimeter’ of circles, and the use
of it became popular ter it was adopted by the Swiss mathematician Leonhard Euler in 1737.
Because it is closely related to the drde, it is found in many formulae from the fields of
geometry and trigonometry, particularly those concerning circles, spheres, or ellipses. Formulae
from other branches of science also indude it in some of their important formulae, including
sciences such as statistics, fractals, thermodynamics, mechanics, cosmology, number theory,
and electromagnetism.
The trigonometric functions that rely on angles, and mathematicians generally, use radians
as units of measurement. P1 plays an important role in angles measured in radians, which are
defined so that a complete circle spans an angle of 2it radians, The angle measure of 180° is
LI IN ICIN ZJ muucwivizçz IN mu IN iWWLJt =
equ to it radians, and
nLUps:/Iuoc-ug--aocsv1ewer.g 009 leuseruollLenL.coIIl/vl
10 =
it/180 radians
In recent years, Pi has been calculated to over one trillion digits passed its decim, Only 39
digits past the decim are needed to accurately cakulate the spheric volume of our entire
universe, but because of Pi’s infinite & pattern less nature, it’s a fun challenge to memorize,
and to computationally cculate more and more digits.
Pi has definitely come a long way in the last few years. It was nice to catch up on my history
involving Pi, I learned a great de about the mathematical necessity and it may have helped m€
gain a greater appreciation of what it is that we do in class.
But mostof all... I loved eating pie.